The 25-year-old signed a long-term contract after a medical on Tuesday.
He will become Liverpool's fourth summer signing after Manchester City's Kolo Toure, Sevilla's Luis Alberto and Celta Vigo's Iago Aspas.
"I am delighted that we have been able to sign one of the top goalkeepers in the Barclays Premier League," manager Brendan Rodgers told the club's website.
"Simon will join a club that will give him an opportunity to demonstrate and improve his huge talent."
The Belgium international has played 101 games for Sunderland sincehis £2m move from Sint-Truiden in June 2010.
He kept 11 clean sheets in 40 matches last season for the Black Cats.
Liverpool's current first-choice keeper Pepe Reina, 30, has been linked with a return to Spanish champions Barcelona, where he started his career.
The Reds have already agreed to sign 32-year-old Manchester City defender Toure on a free transfer and finalised a deal for Celta Vigo striker Aspas, 25, for £7m.
Sevilla midfielder Alberto, 20, has joined the Anfield club for £6.8m, while boss Rodgers is also tracking highly-rated Sporting Lisbon defender Tiago Ilori, 20, and 24-year-old Armenian midfielder Henrikh Mkhitaryan from Shakhtar Donetsk.
